Unifying Tide-Gauge Height Datums With Clock-Derived Potential Differences

National height systems differ by decimetres, and tide gauges inherit those differences, which complicates any global statement about sea level. Spirit levelling ties datums together only by accumulating error with distance. A clock comparison measures a potential difference directly, with an uncertainty that does not grow with distance in the same way. This paper computes the crossover distance at which a centimetre-level clock comparison overtakes levelling, and applies it to representative inter-datum distances. The computed results, taken from the deposited script, are as follows in summary: The computed levelling_error_mm_by_km 50 is 7.07. The computed levelling_error_mm_by_km 200 is 14.1. The computed levelling_error_mm_by_km 500 is 22.4. The computed levelling_error_mm_by_km 1000 is 31.6. The computed levelling_error_mm_by_km 2000 is 44.7. The computed clock_equiv_cm is 1. The computed crossover_km is 100. The computed offsets_typical_cm entry 1 is 5. The computed offsets_typical_cm entry 2 is 30. The study is a computation from stated assumptions, not a measurement, and its figures should be read at the precision those assumptions support.